Question

If a+b+6 and ab=8 then find the value of a^3+b^3 and a^2+b^2

Answer 1

Answer:-

Given:

a + b = 6 -- equation (1).

ab = 8 -- equation (2).

We know that,

a² + b² = (a + b)² - 2ab

(a² + b² = a² + b² + 2ab - 2ab)

Hence,

→ a² + b² = (6)² - 2(8)

→ a² + b² = 36 - 16

→ a² + b² = 20

let , a² + b² = 20. is equation (3)

Now,

a³ + b³ = (a + b)(a² + b² - ab)

Putting the values from equation (1) , (2) , (3).

→ a³ + b³ = (6) (20 - 8)

→ a³ + b³ = 6(12)

→ a³ + b³ = 72.

Hence, a² + b² = 20 and a³ + b³ = 72.